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  • Identical expressions

  • one /(x*ln(x)*ln(ln(x)))
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Sum of series/ 1/(x*ln(x)*ln(ln(x)))

Sum of series 1/(x*ln(x)*ln(ln(x)))


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The solution

You have entered [src] 
  oo                      
 ___                      
 \  `                     
  \            1          
   )  --------------------
  /   x*log(x)*log(log(x))
 /__,                     
n = 2
$$\sum_{n=2}^{\infty} \frac{1}{x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}$$ 
Sum(1/((x*log(x))*log(log(x))), (n, 2, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = \frac{1}{x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
         oo         
--------------------
x*log(x)*log(log(x))
$$\frac{\infty}{x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}$$ 
oo/(x*log(x)*log(log(x)))

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